English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Let $\mathfrak h_t$ be the KPZ fixed point started from any initial conditionthat guarantees $\mathfrak h_t$ has a maximum at every time $t$ almost surely.For any fixed $t$, almost surely $\max \mathfrak h_t$ is uniquely attained.However, there are exceptional times $t \in (0, \infty)$ when $\max \mathfrakh_t$ is achieved at multiple points. Let $\mathcal T_k \subset (0, \infty)$denote the set of times when $\max \mathfrak h_t$ is achieved at exactly $k$points. We show that almost surely $\mathcal T_2$ has Hausdorff dimension $2/3$and is dense, $\mathcal T_3$ has Hausdorff dimension $1/3$ and is dense,$\mathcal T_4$ has Hausdorff dimension $0$, and there are no times when $\max\mathfrak h_t$ is achieved at $5$ or more points. This resolves two conjecturesof Corwin, Hammond, Hegde, and Matetski.

Non-uniqueness times for the maximizer of the KPZ fixed point